If an internet search doesn’t come up with a copy of the manual, I’ll scan the dead tree version and OCR it. The document is then stored in an annex at
~/documents/manuals/. I rarely reference the product manual after initial setup, but when I need it, it’s extremely valuable to have it available – immediately and offline – as a PDF with a searchable text layer.
Some products don’t have manuals, but do have specification sheets. I store these in the same location. Sometimes I’ll just save the product page from the manufacturer’s website as a PDF. This allows me to easily lookup the dimensions of a thing I bought 14 years ago, despite the product being long discontinued by the manufacturer, or the manufacturer no longer existing.